The total amount of such new assessment shall be in such sum as is equitable under all circumstances. It shall in no case exceed that part of the previous assessment that is invalid and is unpaid at the time the ordinance levying the new assessment is introduced, and where, because of lack of competitive bidding, or other cause, the value of the improvement, when made, was less than the contract price thereof, then the new assessment shall not exceed the fair value of the improvement at said time less all payments made on the original assessment and the amount of such part of the original assessment as is valid. And no lot or parcel of land shall be assessed by said ordinance in a greater amount than the difference between the amount of the benefits it shall have received from the improvement and the credits to which it is entitled under section 88.113; provided, however, that if, through error or misconstruction, the amount of the new assessment should, in any case, be excessive under this provision, because of the failure to give a proper credit or credits under section 88.113, the new assessment shall not thereby be avoided, but any person owning or pecuniarily interested in any property which shall not have received due credit under the aforesaid provisions shall be entitled to a proper reduction in amount, in any proceeding brought to enforce such assessment or tax bill, or in appropriate proceedings instituted for the purpose by him or them in the circuit court of the county or city where the property is situated.